Question

On September 30, 2018, the San Fillipo Corporation issued 8% stated rate bonds with a face amount of $480 million. The bonds mature on September 30, 2038 (20 years). The market rate of interest for similar bonds was 10%. Interest is paid semiannually on March 31 and September 30.

Determine the price of the bonds on September 30, 2018.

	Table values are based on: n = i = Cash Flow Amount Present Value Interest Principal Price of bonds

Answer 1

Step 1: Since there are TWO pay periods per year – due to the semiannual interest payments, and it will take TWENTY years for the bonds to mature, we just get to multiply the two together to equal FORTY. 2 * 20 = 40

Step 2 (this step has a tendency to really screw me up when I don’t read the problem closely enough): Look at the second half of the first statement: Corporation C issued 8% stated rate bonds with a face amount of $480 million.

This is where you get your $ amount from, believe it or not. The 8% stated rate is the yearly interest rate for the bonds; however, since the interest is paid SEMIANNUALLY, that’s twice a year btw, the 8% has to be divided by 2in order to the right answer:  8%/2 = .04 (4%).

See, ’cause if you paid 8% on March 31st, then you’d be paying more interest than what is due – which probably is okay in real life . . . hmm, but that’s not what the problem wants you to do.

So then you multiply the FACE AMOUNT of 480 million (that’s a 3 followed by 8 zeros, btw) by the semiannual stated rate of 8%, or better known as8%/2 = .04 (4%). Or put in purely worded equation form:

Face Amount
Stated Rate/2

Numerically stated then:

480,000,000 = 19200000 (which my book refers to as the “annuity amount”)
.04

Step 3!!! – Whoo!

The first part of step 3 we actually completed in step 1. The number of periods is 40; so n = 40. Yay.

We need the interest % now. This time we look to the statement reading: The market rate of interest for similar bonds was 10%. So is it 10%? NOPE. Remember that semiannual thing??? Yup. 10%/2 = 5%

We know that n = 40 and i (interest) = .05 (5%). According to the Present Value Table of an Ordinary Annuity (remember, 480 million was the annuity amount), 17.15909.

Let’s restate what we have so far:

PV = $19200000 * 17.15909 + 480,000,000 (lump sum) * ________ = $ ________

Is it any wonder that it takes me a while to get my homework done?

BTW, the 480,000,000 was given to me in the equation set-up I have. It’s just a plug-in number though, really. From what I can tell, what you do is figure out the interest for the annuity amount, and then do the same thing for the lump sum amount, before finally adding the two together. Meh.

Step 4

Okay, remember the number of periods that we had? 40, right? Remember what i was? 5%, yah? You just plug those two into the regular ol’ Present Value Table now.

= .14205

Our problem now looks like this: PV = $19200000 * 17.15909 + 480,000,000 (lump sum) * .14205 =

Step 5 (Bringing it Together)$19200000 * 17.15909 = 329454528
$480000000 * .14205 = 68184000

329454528 + 68184000 = 397,638,528